Consider the relations $R_1$ and $R_2$ defined as $a\,R_1\,b \iff a^2 + b^2 = 1$ for all $a,b\in\mathbb{R}$, and $(a,b)\,R_2\,(c,d) \iff a + d = b + c$ for all $(a,b),(c,d)\in\mathbb{N}\times\mathbb{N}$. Then: